NIST Special Publication 1088
Maintenance, Validation, and
Recalibration of Liquid-in-Glass
Thermometers
C. D. Cross
W. W. Miller
D. C. Ripple
G. F. Strouse
i
NIST Special Publication 1088
Maintenance, Validation, and
Recalibration of Liquid-in-Glass
Thermometers
C. D. Cross
W. W. Miller
D. C. Ripple
G. F. Strouse
Thermometry Group, Process Measurements Division
Chemical Science and Technology Laboratory
January 2009
U.S. Department of Commerce
Carlos M. Gutierrez, Secretary
National Institute of Standards and Technology
Patrick Gallagher, Deputy Director
ii
Certain commercial entities, equipment, or materials may be identified in this
document in order to describe an experimental procedure or concept adequately. Such
identification is not intended to imply recommendation or endorsement by the
National Institute of Standards and Technology, nor is it intended to imply that the
entities, materials, or equipment are necessarily the best available for the purpose.
National Institute of Standards and Technology Special Publication 1088
Natl. Inst. Stand. Technol. Spec. Publ. 1088, 32 pages (February 2009)
CODEN: NSPUE2
iii
Abstract
Liquid-in-glass thermometers are pervasive throughout industry. These thermometers provide a
convenient method for measuring temperature over a broad range of applications with reasonable
stability and accuracy. However, like all thermometers, liquid-in-glass thermometers are subject
to drift as a function of time and maximum temperature of use. This paper describes methods for
the validation and recalibration of previously calibrated liquid-in-glass thermometers to maintain
the metrological traceability established with the initial calibration. Procedures and examples are
given for visually inspecting a thermometer, using an ice point for a single-point recalibration,
and determining uncertainties for thermometers with a single-point recalibration. We discuss
when a single-point recalibration is acceptable, and when a full recalibration is needed.
Key words: bulb-volume change, calibration, ice point, liquid-in-glass thermometer, mercury
thermometer, organic thermometer, recalibration, thermometer, validation.
Table of Contents
1. Introduction................................................................................................................................. 1
2. Description of liquid-in-glass thermometers .............................................................................. 2
3. Causes of instrument drift........................................................................................................... 4
4. Periodic maintenance plan .......................................................................................................... 5
5. Visual inspection......................................................................................................................... 6
6. Joining separated columns .......................................................................................................... 8
6.1
Mercury-filled thermometers .......................................................................................... 8
6.2
Organic-filled thermometers......................................................................................... 10
7. Testing and recalibration at the ice point.................................................................................. 11
7.1 Preconditioning ................................................................................................................... 11
7.2 The ice point as a reference point ....................................................................................... 11
7.4 Recalibrating liquid-in-glass thermometers—Method I ..................................................... 12
7.5 Recalibration of liquid-in-glass thermometers—Method II ............................................... 13
7.6 Recommended recalibration interval .................................................................................. 15
7.7 Preparation of an ice point .................................................................................................. 15
7.8 Reading thermometers at the ice point................................................................................ 16
7.9 Uncertainties with correction.............................................................................................. 19
8. Organic-liquid thermometers .................................................................................................... 22
9. Summary of recommendations ................................................................................................. 22
Acknowledgments......................................................................................................................... 22
References..................................................................................................................................... 23
Appendix A. Analysis of historical data obtained at NIST ......................................................... 24
Appendix B. Validation of correction method at 150 °C and below ........................................... 26
iv
1. Introduction
Liquid-in-glass thermometers have a proven history of convenience, stability, and accuracy for a
broad range of applications. Nonetheless, like all other thermometers, liquid-in-glass
thermometers may drift, resulting in changes of the indicated temperature versus true
temperature.
Reversible thermometer changes include:
•
separation of the liquid column,
•
introduction of gas bubbles into the column or bulb, or
•
temporary bulb volume changes when a thermometer is used shortly after exposure to a
higher temperature.
Irreversible thermometer changes include
•
changes in bulb volume,
•
microscopic alterations in glass geometry at elevated temperature,
•
microscopic cracking,
•
degradation of the thermometer liquid, or
•
obvious physical breakage.
This document presents:
•
methods for visual inspection of thermometers,
•
methods for user validation of thermometers, and
•
guidance for recalibration of thermometers.
The document presumes that the thermometer was originally calibrated by the manufacturer or a
competent laboratory.
The linkage of a measurement back to primary temperature standards is termed metrological
traceability [1]. Traceability to the standards maintained by NIST consists of:
•
maintaining an unbroken chain of measurements back to NIST standards, with
documented measurement uncertainties, and
•
assuring the continued quality of the measurement artifacts used.
Note that many different thermometer types may be used to perform traceable measurements.
Types other than liquid-in-glass thermometers include platinum resistance thermometers
(abbreviated PRTs, or RTDs for resistance temperature detectors), thermistors, and
thermocouples. The user should carefully consider the best choice of thermometer type for a
given application [2].
Several steps are necessary to assure the continued validity of the calibration results of a liquidin-glass thermometer. There are three separate checks, applied in various combinations for
different thermometer types:
1. visual inspection to ensure that the liquid column has not separated or the thermometer
has not otherwise degraded,
2. calibration at the ice point (or another point on the low end of the scale), and
3. full recalibration.
1
For mercury-filled thermometers used at temperatures of 200 °C and below, a single point
recalibration at the ice point (0 °C) may be used, and a full recalibration is not necessary.
However, for thermometers with contraction chambers and fine graduations, full recalibration is
likely necessary for the best performance. Thermometers used at temperatures of 300 °C and
above are known to undergo changes in the capillary glass, leading to significant drift in
indications; periodic recalibrations are needed for these thermometers. In the temperature range
200 °C to 300 °C, little data on the reliability of a single-point recalibration are available; we
recommend periodic recalibration for this usage range as well. Additionally, little data are
available for plastic-coated thermometers, and we recommend periodic recalibration for this type
of thermometer. Because the thermal expansion of plastics do not match that of glass, coatings
may cause unpredictable changes in thermometer readings, especially for high-precision work.
NOTE: Extreme care must be taken when working with mercury thermometers to avoid
breakage of the thermometer. Operators should be familiar with the health risks of
mercury, and with laboratory policies and safety procedures in the event of a mercury spill.
Mercury is a potent neurotoxin and is categorized as a hazardous material. The U.S.
Environmental Protection Agency [3] and the Occupational Safety and Health
Administration [4] provide additional information on health and environmental hazards,
and control of those hazards.
Thermometers filled with organic liquids present special issues that could result in aging
behavior different than mercury-filled thermometers:
•
the smaller ratio of bulb volume to capillary volume may amplify any changes in the
capillary;
•
the organic liquids may be less chemically stable than mercury, especially at elevated
temperatures; and
•
the interaction of the liquids with the capillary wall may change.
The methods for visual inspection and checks at the ice point provide users valuable tools to
check the performance of organic-filled thermometers, but we do not recommend the single point
recalibration of organic liquid filled thermometers at this time. Research on this topic is still
needed.
The recommendations in this document are based on the data contained in Appendices A and B.
This document supersedes NIST Special Publication SP819 [5].
2. Description of liquid-in-glass thermometers
In this section, we give a brief description of various types of liquid-in-glass thermometers (see
Refs. [6,7] for more details). Liquid-in-glass thermometers consist of a liquid contained in a
glass envelope. Figure 1 provides an illustration of thermometer features and pictures of various
construction types. The glass envelope has a bulb, which is placed in the region where the
temperature is to be measured, and a narrow, graduated capillary, which is part of the
thermometer stem. The liquid has a higher thermal expansion than the glass. As the temperature
2
a)
b)
c)
d)
e)
Fig. 1. Schematic showing the parts of a liquid-in-glass thermometer and pictures of various construction
combinations for both partial and total immersion thermometers: a) principal features of a liquid-in-glass
thermometer, b) partial immersion thermometer with an auxiliary scale, contraction chamber, and
immersion line, c) partial immersion thermometer with no auxiliary scale and no contraction chamber, d)
total immersion thermometer with an auxiliary scale and contraction chamber, and e) total immersion
thermometer with no auxiliary scale and no contraction chamber.
3
increases, expansion of the liquid in the bulb forces the liquid to rise in the capillary. Reading
the liquid meniscus position on the scale provides the measured value of temperature. If the
thermometer is calibrated, an additional correction accounting for the error of the thermometer is
added to the measured value.
When a partial-immersion thermometer is used, the bulb and the portion of the stem up to the
immersion line should be exposed to the temperature being measured, with the remainder of the
stem exposed to ambient conditions. When a total immersion thermometer is used, the bulb and
the entire portion of the stem containing liquid, except for the last 1 cm, are exposed to the
temperature being measured.
The thermal expansion of the liquid contained in the stem of the thermometer significantly
affects the thermometer reading. Because the stem of a partial-immersion thermometer is not
maintained at a controlled temperature, partial-immersion thermometers have a greater
sensitivity to variations in ambient temperature and generally poorer reproducibility than totalimmersion thermometers. The sensitivity to ambient temperature is approximately a factor of 6
higher for thermometers filled with organic liquids than for mercury-filled thermometers. Use of
either a partial- or total-immersion thermometer at an incorrect immersion can result in large
measurement errors, due to the incorrect stem temperature.
The expansion chamber reduces the pressure rise inside the thermometer as the liquid rises up
the scale. Some thermometers feature a contraction chamber, which allows a reduction in the
length of the stem. An auxiliary scale, separated from the main scale by a contraction chamber,
allows measurement at the ice point to check for changes in the bulb volume.
3. Causes of instrument drift
Like all temperature measuring devices, a liquid-in-glass thermometer may indicate different
values at a given temperature over a period of time. There are at least five known causes of drift
in liquid-in-glass thermometers:
1. Change in bulb volume,
2. Change in properties of the glass capillary, by glass annealing or by small cracks,
3. Separation of the liquid column,
4. Movement of foreign objects inside of the glass capillary, and
5. Degradation of the liquid.
Bulb volume changes may be either permanent, after extended or high-temperature use, or
temporary. (Temporary bulb-volume changes occur when the thermometer is heated above room
temperature. However, the bulb contracts to or near the original volume within 72 h after cooling
to room temperature. This will be discussed in Sections 7.4 and 7.5.) If the volume of the bulb
expands, the thermometer will give a lower reading at a specified temperature, compared to its
reading with the original bulb volume.
Changes in the volume of the glass capillary are generally negligible for thermometers used
below 150 °C and often tolerable up to 200 °C. At temperatures near 300 °C and above,
irreversible changes in the capillary (and contraction chamber, if present) are common.
4
Separation of the liquid column can be corrected, using the procedures of Section 6. Known
circumstances that promote separation are:
•
use of organic-liquid thermometers above 100 °C or below −100 °C,
•
storage of organic-liquid thermometers in a horizontal position, and
•
shipment of thermometers, or similar rough handling.
Small droplets may also separate from the main column. Again, the procedures of Section 6 can
rejoin these droplets to the main liquid column. Condensation of liquid is sometimes observed
with thermometers filled with organic liquids. If condensation droplets form routinely, one
should consider using a thermometer with a different filling liquid or another type of
thermometer.
Any thermometer that has visible foreign objects inside the glass capillary, such as glass chips or
any other particles, should be removed from service.
Liquid degradation is rare, but the thermometer should be replaced if a change in the color of the
liquid, or any byproducts of liquid oxidation or breakdown in the capillary or bulb are observed.
Mercury sometimes degrades through oxidation, leaving a residue on the capillary wall. The dye
used to color organic liquids sometimes degrades when exposed to sunlight or ultraviolet light.
Any thermometer with a degraded filling liquid should be removed from service.
4. Periodic maintenance plan
All calibrated or certified liquid-in-glass thermometers should be maintained periodically.
Maintenance steps include:
•
visual inspection to ensure that the liquid column has not separated or degraded,
•
visual inspection to ensure that the scale and graduations are still legible over the full scale
length,
•
calibration at the ice point (or another point on the low end of the scale), and
•
full recalibration (instead of, or in addition to, calibration at the ice point).
The interval between visual inspections varies greatly with use. For a thermometer that is
maintained in a vertical position at a steady temperature, there is virtually no likelihood of a
column separation. Thermometers that are routinely shipped or transported, on the other hand,
may need inspection after every transport. Organic thermometers are more likely in general to
separate than mercury thermometers, especially when subjected to temperatures below −100 °C
or greater than +100 °C.
The frequency for performing a single-point recalibration or of a full recalibration depends on
the maximum temperature of use, the duration of use, and the characteristics of the individual
thermometer tested. Noticeable drift in a liquid-in-glass thermometer is most likely to occur in
thermometers that are in steady, rather than intermittent use; are used at elevated temperatures;
or have fine graduation intervals and contraction chambers. At a minimum, even thermometers
used intermittently near room temperature should be checked yearly at the ice point.
Thermometers used steadily at elevated temperatures should be checked much more often, at
least until a history has been established. Section 7.6 discusses a recommended recalibration
interval based on knowledge of a thermometer’s stability at the ice point.
5
Single-point recalibration is valid for mercury-filled thermometers used at temperatures of
200 °C or below. In the case of thermometers with contraction chambers and fine graduations,
full recalibration is likely necessary for the best performance. Thermometers with usage
temperatures above 200 °C require periodic full recalibration. Full recalibration will also give
the lowest possible uncertainties, as discussed in Section 7.9.
When a large change (greater than one scale division for thermometers with graduations of
0.05 °C or larger) in ice-point reading is observed, care should be taken in applying a singlepoint recalibration, especially for conditions of use where a large change in ice-point reading
would not be expected. An additional visual inspection and ice-point reading should be
performed to confirm the results.
5. Visual inspection
Visually detectable thermometer defects can be divided into two categories: manufacturing
defects apparent when the thermometer is new, and defects that appear with use. For new
thermometers, we recommend a single visual inspection for manufacturing defects, including:
•
uneven scale graduations,
•
improper numbering of the scale,
•
other defects in the glass bulb or funnels connecting chambers with the capillary, and
•
the presence of foreign objects in the filling liquid or in the capillary.
Figure 2 shows an example of a foreign object (glass chip) in the glass capillary.
Fig. 2. Example of a foreign object (glass chip with the red circle) in the glass capillary.
We recommend periodic visual inspections for thermometer defects that may appear with use,
including:
•
degradation of the filling liquid,
•
cracks or other degradation of the glass,
•
loss of scale or numbering legibility, and
•
separation of the liquid column.
See Section 3 for details.
6
Large errors can occur if gas bubbles are introduced into the thermometer bulb or if the liquid
column separates. Thermometers should be visually inspected for these two conditions regularly.
A visual inspection is recommended prior to all calibrations, after any preconditioning step.
Figure 3 shows examples of separated liquid columns. Visually, mercury oxidation may appear
to be column separations that cannot be rejoined, or as a brownish discoloration near the mercury
meniscus.
To inspect a thermometer, place the thermometer on a flat surface with good illumination. Use a
hand magnifier or low-power microscope (10X), and scan for defects along the full length of the
thermometer. As shown in Figure 4, rotate the long axis of the thermometer 360° at the bulb and
at any contraction chambers.
a)
b)
Fig. 3. Example of a separated liquid column indicated by the red oval: a) mercury thermometer and b)
organic thermometer.
Fig. 4. Visual inspection of a liquid in glass thermometer using a low-power microscope (10X).
7
6. Joining separated columns
Sections 6.1 and 6.2 describe methods for joining separated columns observed in mercury-filled
and organic-filled thermometers, respectively. Success in using these methods requires practice,
care in execution, and attention to laboratory safety. Inexperienced users may wish to consult
the manufacturer or an experienced calibration laboratory for assistance.
6.1
Mercury-filled thermometers
NOTE: Extreme care must be taken when working with mercury thermometers to avoid
breakage of the thermometer. Operators should be familiar with the health risks of mercury,
and with laboratory policies and safety procedures in the event of a mercury spill. Mercury is
a potent neurotoxin and is categorized as a hazardous material. The U.S. Environmental
Protection Agency [3] and the Occupational Safety and Health Administration [4] provide
additional information on health and environmental hazards, and control of those hazards.
The process of joining separated mercury columns consists of one or a series of manipulations:
a. The bulb of the thermometer may be cooled in a solution of common salt, ice, and water (or
other cooling agent) to bring the mercury slowly down into the bulb. No more than the
bottom half of the bulb should be cooled and never the stem or mercury column. Moderate
tapping of the bulb on a rubber stopper or similar soft spongy object usually serves to unite
the mercury in the bulb. If the salt solution does not provide sufficient cooling, carbon
dioxide snow (finely crushed dry ice) or a small container of alcohol cooled with dry ice may
be used. Figure 5 shows a mercury thermometer bulb cooled in dry ice to join a separated
mercury column. Since the temperature of dry ice is about −78 °C and mercury freezes at
about −39 °C, the mercury will solidify. To prevent breakage of the thermometer, do not
allow the mercury to freeze within the thermometer bulb. On warming, care must be taken to
warm the top of the bulb first so that pressure in the bulb due to the expanding mercury may
be relieved.
Fig. 5. The bottom portion of a mercury thermometer bulb is being cooled in dry ice to join a separated
mercury column. Note: to prevent breakage, do not let the mercury freeze in the thermometer bulb.
8
b. The mercury can sometimes by reunited by warming the bulb until the column reaches
the separated portion in either the contraction chamber or the expansion chamber. If this
procedure is used, never heat the bulb in an open flame, which could cause rapid heating and
possible bulb breakage, or permanent damage to the bulb if it survives heating. Heat the
thermometer only in a temperature-regulated stirred-liquid bath. Never use a liquid bath at a
temperature greater than the flash point of the bath fluid. Great care is needed to avoid filling
the expansion chamber with mercury, which might produce pressure great enough to burst
the bulb. The expansion chamber should never be more than two-thirds full. Joining the
mercury is more readily accomplished if the quantity in either cavity has first been divided
into droplets by tapping the thermometer gently against the hand. This method should only
be attempted by experienced users with the proper laboratory equipment.
As shown in Fig. 6, to remove a droplet of mercury at the top of the thermometer above the
graduated scale (if graduated above 260 °C), turn the thermometer upside down in a hot,
stirred-liquid bath near 250 °C and vaporize the droplet back toward the main scale. After the
thermometer cools (right side up), the bulb can be heated to allow the main column to pick
up the droplet, which is now in the capillary (on scale). Never heat the thermometer above
260 °C, and never use a liquid bath at a temperature greater than the flash point of the bath
fluid. This method should only be attempted by experienced users with the proper laboratory
equipment and attention to proper safety protocols.
Fig. 6. Heating a mercury thermometer upside down in a liquid bath near 250 °C to join a separated
mercury column. A second thermometer is used to monitor the bath temperature.
9
Gas bubbles, which are sometimes found along the surface of the mercury in the thermometer
bulb, may be collected by circulating, or “washing,” a large gas bubble around the inside of the
bulb (small bubbles will combine with the large bubble). As outlined in method a) above, bring
all of the mercury into the bulb. Hold the thermometer in a horizontal position and gently tap the
thermometer against the hand to form a large gas bubble. Force the bubble to travel around the
wall of the bulb by rotating the thermometer and tapping it against the palm of the hand. When
the entire surface has been “washed,” rotate the bubble to the top of the bulb and reunite the
mercury as described above. It may be necessary to cool the mercury in dry ice (see above) to
release the large gas bubble back into the stem. Success with this method requires practice at
generating one large bubble and not more smaller bubbles.
Fig. 7. Example of a gas bubble being washed out of the mercury in the thermometer bulb. The
red circle indicates the gas bubble.
All of these manipulations require patience (and experience is helpful), but they will generally
yield the desired results if care is used. If the procedures are not successful, do not risk breakage
of the thermometer by deviating from the procedures given above.
6.2
Organic-filled thermometers
The process of joining separated organic-liquid columns is similar to the procedures for mercury
filled thermometers, with only minor changes. Recommended procedures include:
a. The bulb of the thermometer may be cooled to bring the organic liquid slowly down into the
bulb. The cooling agent should be selected so that thermometer bulb is subject to a
temperature cold enough to draw the liquid down into the thermometer bulb, but not so cold
as to cause rapid freezing of the bulb liquid. A mixture of regular ice and salt will attain a
minimum temperature of −21 °C (at a salt concentration of 23 % by weight); crushed dry ice
will reach −78 °C; and liquid nitrogen will reach −196 °C. A stirred liquid bath may also be
used. A cooling agent should be chosen with a temperature at least 20 °C lower than the
lowest graduation on the thermometer. Only the bulb should be cooled and never the stem or
liquid column. Moderate tapping of the bulb on a rubber stopper of similar soft spongy object
usually serves to unite the liquid in the bulb. To prevent breakage of the thermometer, do not
allow the organic liquid to freeze within the thermometer bulb. During warming, care must
be taken to heat the top of the bulb first so that pressure in the bulb due to the expanding
liquid may be relieved.
10
b. The organic liquid can sometimes by reunited by warming the bulb until the column
reaches the separated portion in either the contraction chamber or the expansion chamber. If
this procedure is used, never heat the bulb in an open flame, which could cause rapid heating
and possible bulb breakage, or permanent damage to the bulb if it survives heating. Heat the
thermometer only in a temperature-regulated stirred-liquid bath. Never use a liquid bath at a
temperature greater than the flash point of the bath fluid. Great care is needed to avoid filling
the expansion chamber with the organic liquid, which might produce pressure great enough
to burst the bulb. The expansion chamber should never be more than one-half full. This
method should only be attempted by experienced users with the proper laboratory equipment.
All of these manipulations require patience (and experience is helpful), but they will generally
yield the desired results if care is used. If the procedures are not successful, do not risk breakage
of the thermometer by deviating from the procedures given above.
7. Testing and recalibration at the ice point
7.1 Preconditioning
There is some evidence that liquid-in-glass thermometers, if left unused for several months, will
give readings on first heating that differ from readings on subsequent heatings. Consequently, if
a liquid thermometer is not known to have been used recently and has a maximum temperature
of use of 150 °C or greater, it should be thermally cycled prior to recalibration. We recommend
heating the thermometer to the temperature of maximum use, holding it at that temperature until
the bulb has heated to within 1 °C of its equilibrium temperature, and then cooling to room
temperature. After the preconditioning cycle, wait 72 h prior to recalibration.
For thermometers used above 300 °C, we recommend that measurements at the ice point be
incorporated into this procedure, as a check on the stability of the thermometer:
•
measure the ice point;
•
heat the thermometer to the temperature of maximum use, holding it at that temperature
until the bulb has heated to within 1 °C of its equilibrium temperature;
•
cool to room temperature
•
rest the thermometer at ambient environmental conditions for 72 h (hours); and
•
re-measure the ice point.
If the ice-point measurements do not agree to within one scale division, then the thermometer is
rejected for calibration and use.
7.2 The ice point as a reference point
For many liquid-in-glass thermometers, especially those used at temperatures below 200 °C,
long term changes in the thermometer readings at a given temperature are predominantly a direct
result of changes in the bulb volume. To compensate for this change in the bulb, it is only
necessary to determine the magnitude of the change on the thermometer scale in order to
recalibrate it. This is done by checking at any one of the temperatures that was used as a
calibration point. The point used most often is the ice point, 0 °C (32 °F), consisting of crushed
11
ice and water in an insulated flask, as described in Section 7.7. The ice point is recommended as
a secondary “fixed point” for calibration of thermometers approximating the International
Temperature Scale of 1990 [8,9] and can be reproduced in any laboratory with an expanded
uncertainty (k = 2) of approximately 0.002 °C [10], provided that the methods in Ref. [10] are
followed. (Sections 7.6 and 7.7 provide a description of the preparation and use of an ice point.)
When the ice point is properly realized, the calibration uncertainty of a liquid-in-glass
thermometer is limited by the repeatability of the thermometer, which is typically much larger
than the uncertainty of the ice-point temperature.
7.3 Shape of correction curve
The shape of a correction versus temperature plot for a given liquid-in-glass thermometer is not
affected by a bulb volume change, provided that there are no changes to the capillary volume.
The only change is a shift along the temperature axis (the ordinate), as shown in Fig. 8.
0.25
New correction for ice-point change
0.20
Original correction
Correction, °C
0.15
0.10
0.05
0.00
-0.05
-20
0
20
40
60
80
100
120
Temperature, °C
Fig. 8. Recalibration plot of corrections versus temperatures for a given liquid-in-glass thermometer.
Lines connect calibration points to aid in interpolation between points.
7.4 Recalibrating liquid-in-glass thermometers—Method I
Before the bulb-volume change is determined by observing the scale reading at the ice point or at
another calibration temperature, the thermometer must remain at room temperature for 72 h. This
is necessary because a temporary, reversible change will occur in the volume of the bulb if the
thermometer is heated beyond room temperature. This temporary expansion of the bulb will
introduce an error in the reading, since most thermometers are initially calibrated by starting at
the lowest temperature (usually 0 °C) and proceeding to the higher temperatures. This heating of
12
the thermometer from the lowest point to the highest point will cause gradual expansion of the
bulb.
For the following examples, the ice point is used as the recalibration point, since, in practice, it is
the one most often used in recalibrations. After the thermometer has been at room temperature
for 72 h, an ice-point measurement is recorded (from which the ice-point correction is
calculated) and compared to the ice-point measurement that was determined the last time the
thermometer was calibrated or recalibrated. If the ice-point reading is found to be higher or lower
then the previous reading, all other readings will be higher or lower, respectively, by the same
amount. Examples are given in Table 1 and in Fig. 8
Table 1. Recalibration of liquid-in-glass thermometers using the ice point.
Calibration
Point, °C
0
50
100
150
Original
Correction, °C
New Correction
For Ice-Point Change, °C
−0.05°C
+ 0.10
+ 0.22
+ 0.07
Calibration
Point, °C
Original
Correction, °C
−50
0
50
100
−0.03
−0.10
+ 0.15
+ 0.23
−0.10 °C
+ 0.05
+ 0.17
+ 0.02
New Correction
For Ice-Point Change, °C
+ 0.07
0.00
+ 0.25
+ 0.33
7.5 Recalibration of liquid-in-glass thermometers—Method II
The recalibration method described above is used when the standard liquid-in-glass thermometer
is needed only once or twice a week and the thermometer is used starting from the lowest
temperature point and going to the highest temperature points and not used again for 72 h. Many
times, however, a standard liquid-in-glass thermometer is needed every day and at numerous
temperatures. Temporary changes that occur in the bulb volume make using the thermometer at
any time impossible if corrections generated as in Section 7.4 are to be used. The magnitude of
the ice-point depression increases as the maximum temperature of use increases. The magnitude
also depends on the type of glass used in the thermometer fabrication. The change in reading due
to the temporary bulb-volume change is known as the ice-point depression because the
expanding bulb volume causes the ice-point reading to decrease.
Fortunately, there is a way to compensate for temporary bulb-volume changes. First, the
variation of the thermometer ice-point reading as a function of temperature must be determined.
After the thermometer has remained at room temperature for 72 h, observe the scale reading at
the ice-point and adjust the corrections as described in Section 7.4 to account for the new ice-
13
point reading. We will term these corrections the “current corrections”. Next, heat the
thermometer to within one scale division of the next higher calibration temperature, cool to room
temperature, and then insert it into an ice point. The ice-point reading is observed and recorded.
This is repeated at all of the calibration points in ascending order. The ice-point reading (not
correction) is then added to the current correction at each calibration point, producing what is
called an "adjusted set of scale corrections". An example of how to establish a set of adjustedscale corrections is given in Table 2. This procedure need only be performed once for each
thermometer.
Table 2. Establishing adjusted-scale corrections.
Calibration
Point, °C
0
40
80
120
160
200
Current
Correction, °C
Ice-Point Reading
After Heating to
Calibration Point, °C
−0.10
−0.10
−0.10
−0.15
−0.15
−0.20
+0.10
+0.15
+0.20
+0.15
+0.25
+0.10
Adjusted-Scale
Correction, °C
0.00
+0.05
+0.10
+0.00
+0.10
−0.10
Note that the adjusted-scale correction is only an intermediate step in determining the correction
to be applied in actual use. The recipe for the complete correction is as follows. After use of the
thermometer at a given temperature, cool the thermometer to room temperature, and read the
thermometer in an ice point within 30 min. Subtract this last ice-point reading from the
appropriate adjusted-scale correction to obtain the actual correction.
As an example, suppose we measured the temperature of an oil bath with the thermometer from
Table 2. In the oil bath, we read a temperature of 100.00 °C. The thermometer was removed
from the oil bath, allowed to cool, and then a reading of −0.15 °C was obtained at the ice point.
The bath temperature is calculated as follows:
1. From Table 2, the adjusted-scale correct is +0.05 °C, obtained by linear interpolation of
the values +0.10 °C at 80 °C and 0.00 °C at 120 °C.
2. To obtain the thermometer correction at 100 °C, we subtract the recent ice-point reading
from the adjusted scale factor:
Correction at 100 °C = +0.05 °C – (−0.15 °C) = +0.20 °C.
This gives the total correction that is to be added to the thermometer reading of
100.00 °C.
3. The actual temperature of the oil bath is then 100.00 °C + 0.20 °C = 100.20 °C.
Application of this method, or adherence to the limits of Method I, may not always be practical.
In such circumstances, the magnitude of the ice-point depression may be determined by heating
the thermometer to a given temperature, reading the ice-point value shortly after cooling and
after a 72 h wait, and taking the difference between the two ice-point values to obtain a typical
ice-point depression. If this depression is small relative to the desired measurement uncertainty,
the difference may be taken as an additional component of the standard uncertainty. If, on the
14
other hand, the ice-point depression is large compared to the desired measurement uncertainty,
use of a different thermometer should be considered.
7.6 Recommended recalibration interval
The interval of recalibration of a liquid-in-glass thermometer depends on several factors. If a
thermometer has a large bulb, is used at high temperatures (exceeding 200 °C), or is new, it is
expected that the greatest change will be seen. Initial checks at the ice point may be as often as
once a month. If the ice point shows little change over a period of time, the recalibration interval
can be increased to every two months. If the ice point continues to indicate a stable bulb, within
an acceptable uncertainty, the recalibration interval can be extended to once or twice a year. This
is recommended as the minimum interval between calibration checks.
7.7 Preparation of an ice point
Since the ice point is so important in the recalibration and use of liquid-in-glass thermometers, a
discussion will be given of its preparation. A new ice point should be made every day it is
needed. (We use the term “ice point” to describe the physical realization of the ice melting point.
The terms “ice bath” and “ice-point bath” describe the same realization.)
The ice, from which to prepare the ice point, can be made from distilled or de-ionized water, or it
can be the clear portion of commercially-available ice, which is frozen from the outside inward,
leaving the impurities in the center. The ice is shaved to the consistency of that used in a "snow
cone", with particles of 2 mm to 5 mm in diameter. The ice is placed in the Dewar flask with
distilled water and packed firmly. Put as much ice in the flask as possible and fill the crevices
with distilled water. Cover the surface of the ice with an opaque cover (a dark colored piece of
felt is adequate. After approximately 15 min to 30 min, excess water, resulting from the melting
of the ice, is siphoned from the flask and ice is added to replace that which has melted. The ice
point is ready to use when it has set for 15 min to 30 min, the ice should be saturated with
distilled water, but the ice should not float in the flask, and there is no excess water on the
surface of the ice. If more than a few thermometer measurements are to be made, a siphon tube is
placed at the bottom of the flask to remove excess water that will be produced by melting of the
ice. Throughout the day, replace the siphoned water with ice. Preparation of an ice point used at
NIST is shown as Fig. 9.
15
a.
c.
b.
d.
Fig. 9. Preparation of an ice point: a) shaved ice particles, b) siphon tube inserted into Dewar flask, c)
packing a Dewar flask with shaved ice and water, and d) completed ice point.
7.8 Reading thermometers at the ice point
An ice-point reading is observed on a thermometer by inserting the thermometer in an ice point
that has been prepared as described in Section 7.7. The ice and water must be kept free from
contaminates. The thermometer should be cleaned before being inserted into the ice and the
operator's hands should be freshly washed or plastic gloves worn. This is necessary to prevent
foreign material, especially perspiration salt from the hands, from being introduced into the ice
point. If the thermometer is rinsed before being inserted into the ice, always use distilled water at
room temperature or colder, since warm water will expand the bulb and give an erroneous icepoint reading. The ice at the center Dewar flask is loosened with a clean glass or metal rod to a
depth approximately equal to the thermometer's immersion depth. Figure 10 shows how a
thermometer and an ice point are prepared prior to a measurement.
16
a.
b.
c.
d.
Fig. 10. Preparing a thermometer for measurement at the ice point: a) cleaning the thermometer with
shaved ice, b) pre-chilling the thermometer prior to insertion into the ice point, c) creating a hole for the
thermometer in the ice point with a clean metal rod, and d) inserting thermometer to its proper immersion.
Gently place the thermometer through the holder and into the region of loosened ice. If the
thermometer touches a firm surface before it is immersed to the immersion line or 0 °C mark,
then remove the thermometer and loosen the ice further down into the Dewar flask to permit the
thermometer to be immersed to the proper depth (see Fig. 1 and Fig. 11). If the immersion line
or 0 °C mark on the thermometer passes below the surface of the ice before resting on a firm
foundation, remove the thermometer, repack the ice, and loosen the ice to the correct depth. The
flask must be sufficiently deep to ensure that at least 3 cm of ice-water mixture are between the
bottom of the thermometer bulb and the bottom of the flask. When the thermometer is properly
immersed and perpendicular to the measurement device (e.g., digital video camera, telescope,
magnifier, eye), firmly pack the ice around the thermometer to the immersion line or
approximately 1 cm below the 0 °C mark, the thermometer is ready to be read.
17
a.
b.
Fig. 11. Proper immersion depth of a thermometer in an ice point: a) partial immersion and b) total
immersion.
The thermometer should remain in the ice point for approximately three minutes. (Thermometers
using an organic liquid instead of mercury as the thermometric fluid will require approximately
15 mins, or even longer at the lowest temperatures, to attain a stable reading because the organic
fluid drains slowly from the wall of the capillary.) When stability is reached (the meniscus stops
moving) for mercury thermometers, gently tap the thermometer to free the mercury meniscus
(which can sometimes stick) and record the ice-point reading. For thermometers with a scale
graduation of 0.01 °C or less, a soft plastic rod, or something of similar compliance, is placed
near the point to gently tap mercury thermometers before reading.
If a magnifier is used, it should be designed for use with liquid-in-glass thermometers, its mount
should hold the lens perpendicular to the thermometer stem, and its mounting should not prevent
proper immersion of the thermometer into the ice point. When using a magnifier, the calibrator
must read the thermometer with a direction of vision perpendicular to the thermometer.
Otherwise, parallax error may be significant.
Partial-immersion thermometers that meet ASTM specification E1 require a stem-temperature
correction. These thermometers will have an immersion depth and the letters “ASTM” on the
back of the thermometer. Refer to the appropriate ASTM standards [7,11] for additional
guidance.
18
7.9 Uncertainties with correction
The use of a single-point recalibration at the ice point adds an additional uncertainty to the
updated thermometer calibration result at every temperature but the ice point. There is a simple
relation between the original and adjusted thermometer correction at temperature t:
C (t ) = C orig (t ) + C 0 − C orig, 0
(1
where C(t) is the correction at temperature t at the time of recalibration, Corig(t) is the correction
of the original calibration, C0 is the ice-point reading at the time of recalibration, and Corig,0 is the
ice-point reading of the original calibration.
This measurement equation then leads to the standard uncertainty u(C) for a thermometer
correction C at temperature t:
[
u (C ) = u (Corig ) 2 + s 2 + sorig
2
]
1/ 2
,
(2
where u(Corig) is the standard uncertainty of the original calibration at a given temperature t, s is
the short-term repeatability at the ice point as measured by the user, and sorig is the short-term
repeatability at the ice point for the original calibration.
The value of u(C) and s depend on the properties of the thermometer and the skill of the operator
in reading the thermometer. A properly prepared ice point contributes a relatively small
component to u(C). For a given thermometer, the value of s can be estimated by repeat
measurements of the ice point over several days.
As an alternative, values of s for mercury-filled thermometers may be estimated based on
literature values of liquid-in-glass thermometer uncertainties [12] and on the resolution of
various methods to read thermometers. Typical reading resolutions for various methods are
listed in Table 2. From Ref. [12], values of s obtained with a video readout may be
approximated as s = 0.02 °C for temperatures less than 100 °C, and s = 0.04 °C for temperatures
between 100 °C and 200 °C. (For thermometers graduated in Fahrenheit, the equivalent values
are s = 0.036 °F for temperatures less than 212 °F, and s = 0.072 °F for temperatures between
212 °F and 392 °F.) A general recipe for the value of s is to take the maximum of the literature
values and the resolution values in Table 3. Tables 4 and 5 give results for thermometers in
degrees Celsius and degrees Fahrenheit, respectively. The values in these tables are only
guidelines; repeatability data obtained in other laboratories may be used instead.
Table 3. Typical resolutions for various methods of reading liquid-in-glass thermometers.
Method
Video camera
Telescope
Magnifier
Naked eye
19
Reading resolution
0.03 graduation
0.05 graduation
0.10 graduation
0.25 graduation
Table 4. Approximate values for ice-point repeatability (either s or sorig) for thermometers graduated in
degrees Celsius.
Maximum usage temperature less than 100 °C
Reading method
Graduation
(°C)
0.05, 0.1
0.2
0.5
1
2
Video
s, (°C)
0.02
0.02
0.02
0.02
0.04
Telescope
s, (°C)
0.02
0.02
0.03
0.05
0.10
Magnifier
s, (°C)
0.02
0.02
0.05
0.10
0.20
Naked
Eye
s, (°C)
0.03
0.05
0.13
0.25
0.50
Maximum usage temperature less than 200 °C
Reading method
Graduation
(°C)
0.05, 0.1
0.2
0.5
1
2
Video
s, (°C)
0.04
0.04
0.04
0.04
0.04
Telescope
s, (°C)
0.04
0.04
0.04
0.05
0.10
Magnifier
s, (°C)
0.04
0.04
0.05
0.10
0.20
Naked
Eye
s, (°C)
0.04
0.05
0.13
0.25
0.50
Table 5. Approximate values for ice-point repeatability (either s or sorig) for thermometers graduated in
degrees Fahrenheit.
Maximum usage temperature less than 212 °F
Reading method
Graduatio
Video
Telescope
Magnifier
n
(°F)
s, (°F)
s, (°F)
s, (°F)
0.1
0.04
0.04
0.04
0.2
0.04
0.04
0.04
0.5
0.04
0.04
0.05
1
0.04
0.05
0.10
2
0.04
0.10
0.20
Naked Eye
s, (°F)
0.04
0.05
0.13
0.25
0.50
Maximum usage temperature less than 392 °F
Reading method
Graduatio
Video
Telescope
Magnifier
n
(°F)
s, (°F)
s, (°F)
s, (°F)
0.1
0.07
0.07
0.07
0.2
0.07
0.07
0.07
0.5
0.07
0.07
0.07
1
0.07
0.07
0.10
2
0.07
0.10
0.20
Naked Eye
s, (°F)
0.07
0.07
0.13
0.25
0.50
20
These tables apply to thermometers that have graduation lines approximately 0.5 to 1.0 mm
apart, typical of many thermometers defined in ASTM E 1 [7]. Thermometers with closer
graduation lines, such as those that meet the obsolete SAMA specification [13], will have higher
values of s. Thermometers with wider separations may have smaller values of s.
Note that the calibration uncertainties described above may not fully account for the
uncertainties in actual use. A user often may not be able to read the thermometer at the same
resolution as obtained in the calibration. Also, the readings of partial immersion thermometers
depend on the temperature of the liquid column, as described in Ref. [6], and the effect can be
quite large for thermometers filled with organic liquids and/or used at elevated temperatures.
Example
A thermometer with maximum usage temperature of 125 °C and 1 °C graduations has an
expanded uncertainty (k = 2) of 0.25 °C for the original calibration. The original calibration used
a telescope. What is the revised calibration uncertainty if recalibrated at the ice point, using a
magnifier?
The original uncertainty is divided by two to obtain the standard (k = 1) uncertainty:
0.25 °C
u (C orig ) =
= 0.125 °C .
(3
2
The values of ice-point repeatability are taken from Table 2: sorig = 0.05 °C and s = 0.10 °C. The
standard uncertainty of the recalibrated thermometer is determined by summing in quadrature
u(Corig), sorig, and s, using Eq. 2:
[
]
u (C ) = (0.125 °C) 2 + (0.05 °C) 2 + (0.10 °C) 2 = 0.17 °C .
Finally, the standard uncertainty is multiplied by two to obtain the expanded uncertainty:
U (C ) = 2u (C ) = 0.34 °C
(4
(5
Tables 4 and 5 give typical calibration uncertainties and values of s for mercury-in-glass
thermometers [9].
If the user is unable to perform periodic calibrations at the ice point with a sufficiently low
uncertainty, then periodic recalibration by a competent calibration laboratory will be necessary.
This calibration may be solely at the ice point for mercury-filled thermometers with a maximum
usage temperature of 200 °C or less, with calibration uncertainty as described in section 7.9. If
these measurements indicate significant drift in the thermometer, a full recalibration will be
necessary to determine the thermometer corrections at intermediate temperatures. As a final
alternative, all of the points of the original calibration may be repeated. In either case, an
allowance for variation in the ice point should be included in the user’s uncertainty budget, based
on the variation observed between the original and subsequent calibration results.
21
8. Organic-liquid thermometers
Periodic visual inspection and measurement at the ice point serve as a valuable measurement
assurance tool for organic-liquid thermometers. However, the procedures described in this
document for single-point recalibration have not been validated for organic liquid thermometers
and is not recommended at the time of this publication. There are several reasons why organic
liquids may be more susceptible to drift than mercury-filled thermometers:
•
the smaller ratio of bulb volume to capillary volume may amplify any changes in the
capillary;
•
the organic liquids may be less chemically stable than mercury, especially at elevated
temperatures; and
•
the interaction of the liquids with the capillary wall may change with time.
9. Summary of recommendations
When properly cared for, liquid-in-glass thermometers can give excellent, repeatable results at a
low instrument cost. A common misconception is that these thermometers require no periodic
recalibration or validation.
Mercury thermometers require:
•
visual inspection,
•
periodic checks at the ice point (single-point recalibration), if used at temperatures below
200 °C, and
•
full recalibrations, if used at temperatures of 200 °C and above, if the thermometer has a
contraction chamber and fine graduations, or if the ice-point check shows changes that are
large compared to the thermometer uncertainty.
The interval between full recalibrations is best determined by past history of the thermometer
and the user’s tolerance on the measurement uncertainty (as described in Section 7.6).
Organic thermometers require:
•
visual inspection, and
•
full recalibrations, or validation of the original calibration at the highest and lowest
temperatures of use.
In all cases, checks at the ice point can be a useful intermediate check between full
recalibrations. However, single-point recalibration has not been validated for organic liquid
thermometers and is not recommended at the time of this publication
Visual inspection and measurements at the ice point can be performed by the user.
Acknowledgments
We thank the members of ASTM committee E20.05 on Liquid-in-Glass Thermometers and
Hydrometers for their helpful comments.
22
References
[1]
International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM),
3rd edition, JCGM 200:2008 (BIPM, Sèvres, France, 2008).
[2]
Ripple, D. C., and Strouse, G. F., “Selection of Alternatives to Liquid-in-Glass Thermometers,” J.
ASTM International 2, JAI13404 (2005).
[3]
Website http://www.epa.gov/mercury/ accessed on Dec. 16, 2008.
[4]
Website http://www.osha.gov/SLTC/mercury/ accessed on Dec. 16, 2008.
[5]
Wise, J. A., “A Procedure for the Effective Recalibration of Liquid-in-Glass Thermometers,” NIST
SP 819 (National Institute of Standards and Technology, Gaithersburg, MD, 1991).
[6]
Wise, J. A., “Liquid-in-Glass Thermometer Calibration Service,” NIST SP 250-23 ((National
Institute of Standards and Technology, Gaithersburg, MD, 1988).
[7]
ASTM E 1-07, “Standard Specification for ASTM Liquid-in-Glass Thermometers,” (ASTM, West
Conshohocken, PA, 2007).
[8]
Preston-Thomas, H., “The International Temperature Scale of 1990 (ITS-90),” Metrologia 27, 3-10
(1990); Metrologia 27, 107 (1990).
[9]
Bedford, R. E., Bonnier, G., Maas, H., and Pavese F., “Recommended values of temperature on the
International Temperature Scale of 1990 for a selected set of secondary reference points,”
Metrologia 33, 133-154 (1996).
[10] Mangum, B. W., “Reproducibility of the Temperature of the Ice Point in Routine Measurements,”
NIST TN 1411 (National Institute of Standards and Technology, Gaithersburg, MD, 1995).
[11] ASTM E 11-07, “Standard Test Method for Inspection and Verification of Thermometers,” (ASTM,
West Conshohocken, PA, 2007).
[12] Vaughn, C. D., and Strouse, G. F., “NIST Calibration Uncertainties of Liquid-in-Glass
Thermometers over the Range from -20 °C to 400 °C,” in Temperature: Its Measurement and
Control in Science and Industry, ed. D. C. Ripple et al., Vol. 7, CP684 (AIP Conf. Proc., Melville,
NY, 2003), pp. 447-452.
[13] SAMA/ANSI Z236.1-1986, “American National Standard for Liquid-in-Glass Thermometers—
General Purpose Laboratory Use,” (Scientific Apparatus Maker Association, Alexandria, VA,
1983).
23
Appendix A. Analysis of historical data obtained at NIST
Prior to the common usage of single-point recalibration, NIST routinely performed repeat
calibrations of liquid-in-glass thermometers at multiple points. We have analyzed calibration
data from 24 thermometers calibrated at NIST, plus the 3 thermometers reported in Table 2 of
Ref. [5]—examining whether repeat calibration data can be adequately predicted from the
change in correction at the ice point alone. Table 6 gives an overview of the statistical analysis.
To determine if the correction curves shifted by the same amount as the ice-point reading, as
seen in Fig. 2, we:
1. computed the difference between the correction at each temperature and the ice-point
reading, for each set of calibration results;
2. calculated the standard deviation for all the differences corresponding to a particular
calibration temperature;
3. computed the ratio of the standard deviation to the expected standard uncertainty calculated
using Eq. 2; and
4. identified outliers where the ratio of standard deviation to standard uncertainty exceeded two.
For a few thermometers, there was no auxiliary scale, and thus no ice-point reading. In this case,
we used the lowest calibration point instead of the ice point as a reference state.
Of the 27 thermometers studied, five thermometers indicated possible outliers. Three of these
thermometers had maximum calibration temperatures of 300 °C or higher. One of the
thermometers had very fine graduation intervals relative to its operating temperature, and the
identification as an outlier depended greatly on our assignment of calibration uncertainty. For
the remaining thermometer, with a maximum calibration temperature of 136 °C, the large
standard deviations could be traced to a single discrepant point; we suspect that that point is an
erroneous reading.
From this analysis, we concluded the following:
1. For all thermometers with a maximum calibration temperature of 200 °C or lower,
recalibration at the ice point was valid (with one ambiguous case discussed in Note (d) of
Table 6). However, few of these thermometers showed significant drift in the ice-point
value in any case.
2. The single-point recalibration method dramatically failed for thermometers with
maximum calibration temperatures of 300 °C or above.
3. In the case of thermometers with large contraction chambers and fine graduations, full
recalibration is necessary for the best performance.
24
Table 6. Summary of thermometers used in study of historical data. Thermometers with clear signs of
capillary changes have the maximum calibration temperature in bold font.
Max. cal.
temperature,
°C
Number of
repeat
calib.
Number
of calib.
points
Number
of
outliers
10 Partial Immersion Thermometers
94 °F to 115 °F, in 0.02 °F
−26 °F to 66 °C, in 0.2 °C
−20 °C to 110 °C, in 1 °C
−20 °C to 110 °C, in 1 °C
−20 °C to 110 °C, in 1.0 °C
30 °F to 314 °F in 0.2 °F
98 °C to 200 °C, in 0.5 °C
−5 °C to 200 °C in 0.2 °C
200 °F to 400 °F in 1.0 °F
100 °F to 950 °F, in 5 °F
41
55
56
56
56
99
200
200
204
509
4
3
2
2
5
3
3
3
3
3
6
3
2
1
2
4
3
4
2
2
0
0
0
0
0
0
0
0
1
1
17 Total Immersion Thermometers
19 °C to 35 °C in 0.02 °C
−10 °C to 101 °C in 0.1 °C
−1 °C to 201 °C 0.2 °C
75 °C to 105 °C in 0.1 °C
167 °F to 221 °F in 0.2 °F
204 °F to 220 °F in 0.1 °F
98 °C to 152 °C in 0.1 °C
272.5 °F to 277.5 °F in 0.1 °F, with aux.
99 °C to 201 °C, in 0.1 °C
95 to 155 °C in 0.2 °C, with aux.
−1 °C to 201 °C in 0.2 °C
−2 °C to 205 °C in 0.2 °C
−2 °C to 205 °C in 0.2 °C
295 °F to 400 °F in 0.5 °F, with aux.
295 °F to 400 °F in 0.5 °F, with aux.
30 °F to 580 °F, in 2 °F
30 °F to 760 °F in 2 °F
34.5
40
80
90
99
103.3
110
136
140
145
200
200
200
204
204
300
371
2
2
2
2
2
2
2
4
2
4
4
4
4
4
4
2
2
11
4
3
1
2
4
2
3
2
3
2
11
11
2
1
6
7
0
0
0
0
0
0
0
3 or 0
0
0
0
0
0
0
0
1
4
Type
Notes
(a)
(b)
(c)
(c)
(d)
(b)
(b), (c)
Notes:
(a) Outlier resulted from one anomalous point, most likely a calibration error
(b) Clear evidence of capillary changes
(c) Data from Table 2 of Ref. [5].
(d) This thermometer has a very large contraction chamber, and the value to use for the
calibration uncertainty is not well known. If the calibration uncertainty is based on
thermometers with similar maximum temperature of use in Ref. [11], there are zero outliers.
If the calibration uncertainty is based on thermometers with similar intervals between
graduations in Ref. [11], all three calibration points are outliers.
25
Appendix B. Validation of correction method at 150 °C and below
The data described in Appendix A dates were measured prior to 1985, for all but two
thermometers. To test the performance of modern thermometers, we performed a series of tests
with a set of five, newly purchased ASTM 67C thermometers. These total immersion
thermometers have a scale from 95 °C to 155 °C, with 0.2 °C divisions and a 0 °C auxiliary
scale.
Initial tests gave erratic results, later attributed to a lack of preconditioning (see Section 7.1).
The tests were repeated with another set of preconditioned thermometers, with much better
results. Ice points were acquired 30 min, 24 h, and 72 h after each exposure to high temperature.
All of the data plotted in the figures use the 72 h ice-point readings. The measurement history
was as follows:
1. Two rounds of testing at 110 °C, with a full set of ice-point measurements between rounds.
2. 10 days exposure at 110 °C, followed by 30 days at room temperature.
3. Three rounds of testing at 150 °C, with a full set of ice–point measurements between rounds.
4. 14 days exposure at 150 °C
5. Two rounds of testing at 150 °C, with a full set of ice–point measurements between rounds.
6. Testing at 110 °C, 150 °C, and 110 °C, with a full set of ice–point measurements after the
three points.
Observations with a polariscope before and after measurements showed no visible changes of
strain in the glass stem of the thermometer.
Figure 12 shows the thermometer corrections at 110 °C and 150 °C at various steps in the
thermal history. Note that there is no clear sign of drift in the corrections, even after a 14 d soak
at 150 °C. As confirmation of this observation, the standard deviation of the corrections at 0,
110, and 150 °C were all slightly smaller than the Type A repeatability (k = 1) reported for this
type of thermometer in Ref. [11]. Figure 13 shows the corrections after adjustment for changes
in the 72 h ice-point reading.
To investigate whether correcting for ice-point changes reduces the variance of the corrections at
110 °C and 150 °C, we calculated the standard deviation of both the corrections themselves at
each temperature and the corrections adjusted for changes in the ice point. Table 7 gives the
pooled standard deviations for the set of five thermometers. There is virtually no difference
between the raw corrections and the corrections adjusted for ice-point changes, indicating that
correcting for the ice-point change did neither good nor harm for this particular set of
thermometers.
26
0.2
S/N 4D5070
S/N 4D5071
S/N 4D4072
Correction, °C
0.1
S/N 4B8826
S/N 4B8827
0.0
−0.1
U (k =2)
0
11
0
15
0
11
15
0
0
15
50
ys
at
1
15
0
0
15
0
15
at
1
10
0
11
10
14
da
da
ys
11
0
−0.2
Measurement History
Fig. 12. Corrections at 110 °C and 150 °C (designated by 110 and 150 on the ordinate).
0.2
S/N 4D5070
S/N 4D5071
S/N 4D4072
0.1
S/N 4B8826
Correction, °C
S/N 4B8827
0.0
-0.1
U (k =2)
0
11
0
15
0
11
0
15
0
15
at
ys
da
ys
14
da
10
15
0
0
15
0
15
0
at
15
11
0
0
11
11
0
-0.2
Measurement History
Fig. 13. Corrections at 110 °C and 150 °C (designated by 110 and 150 on the ordinate) adjusted
for changes in the ice-point reading.
27
Table 7. Comparison of pooled standard deviations (SD) for thermometer corrections with and without
adjustment for ice-point changes.
t, °C
100
150
Pooled SD, °C
Without adjustment
With adjustment
0.041
0.038
0.036
0.041
28